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We propose a novel method to test the existence of community structure ofundirected real-valued edge-weighted graph. The method is based on Wignersemicircular law on the asymptotic behavior of the random distribution foreigenvalues of a real symmetric matrix. We provide a theoretical foundation forthis method and report on its performance in synthetic and real data,suggesting that our method outperforms other state-of-the-art methods.

Statistical test for detecting community structure in real-valued edge-weighted graphs